Hey there!
Can you give some more information? Which quest?

It's not a quest. Go to one of the music vendors and then use the shop. You buy the blueprints. Once you have the blueprint or blueprints that you want, click on them to get the option to navigate to the NPC who will give a daily quest for that particular blueprint. It will take at least 10 days for each instrument apart from drums (which is a weekly and all done at the same time). I would recommend Piano first though, as there isn't really any music available on the jukebox for drums.